Consistency relations for sharp features in the primordial spectra

TL;DR

This paper derives a one-parameter consistency relation linking sharp features in the primordial spectra to rapid variations in sound speed and expansion rate during inflation, supported by multiple model examples.

Contribution

It introduces a novel relation connecting sound speed and expansion rate variations, enabling unified analysis of sharp features in primordial spectra.

Findings

Established a one-parameter relation between bispectrum and power spectrum features.

Validated the relation with models exhibiting sudden and resonant features.

Provided a framework for analyzing sharp features in inflationary scenarios.

Abstract

We study the generation of sharp features in the primordial spectra within the framework of effective field theory of inflation, wherein curvature perturbations are the consequence of the dynamics of a single scalar degree of freedom. We identify two sources in the generation of features: rapid variations of the sound speed c_s (at which curvature fluctuations propagate) and rapid variations of the expansion rate H during inflation. With this in mind, we propose a non-trivial relation linking these two quantities that allows us to study the generation of sharp features in realistic scenarios where features are the result of the simultaneous occurrence of these two sources. This relation depends on a single parameter with a value determined by the particular model (and its numerical input) responsible for the rapidly varying background. As a consequence, we find a one-parameter consistency relation between the shape and size of features in the bispectrum and features in the power spectrum. To substantiate this result, we discuss several examples of models for which this one-parameter relation (between c_s and H) holds, including models in which features in the spectra are both sudden and resonant.